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Gradient-free algorithms for distributed online convex optimization |
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| Authors: | Yuhang Liu Wenxiao Zhao Daoyi Dong |
| Affiliation: | 1. The Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China Contribution: ?Investigation, Methodology, Writing - original draft;2. The Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China;3. School of Engineering and Information Technology, University of New South Wales, Canberra, ACT, Australia Contribution: Writing - review & editing |
| Abstract: | In this paper, we consider the distributed bandit convex optimization of time-varying objective functions over a network. By introducing perturbations into the objective functions, we design a deterministic difference and a randomized difference to replace the gradient information of the objective functions and propose two classes of gradient-free distributed algorithms. We prove that both the two classes of algorithms achieve regrets of for convex objective functions and for strongly convex objective functions, with respect to the time index and consensus of the estimates established as well. Simulation examples are given justifying the theoretical results. |
| Keywords: | distributed algorithm gradient-free algorithm multiagent system online convex optimization |